A) You can start with a favorite tongue twister ("Betty Botter"
or "Peter Piper") and suggest that your students revise it.

B) You can ask your students to make lists of words starting
with the same letter or sound they can use in a poem, then suggest
that they write their own tongue twisters.

But no matter how you start, the above method helps your students
tell a story that makes sense, uses lots of tongue-twisting
consonants, and has a pleasing rhythm and rhyme pattern.

Here's a new version of "Betty Botter" I wrote using this method:

Betty Botter's Biting Beaver
Betty Botter bought a beaver.
But the beastly beaver bit her.
So she bought a biting badger.
And the badger bit the beaver.
Since the badger bit the beaver,
now the beaver will not bite her.
So 'twas better Betty Botter
bought a beaver-biting badger.